The characteristic energy and ratio of longitudinal diffusion coefficient to mobility for electrons in hydrogen and

(1)

Journal of Physics D: Applied Physics

RAPID COMMUNICATION

The characteristic energy and ratio of longitudinal diffusion coefficient to mobility for electrons in hydrogen and nitrogen

To cite this article: W Roznerski et al 1990 J. Phys. D: Appl. Phys. 23 1461

View the article online for updates and enhancements.

Recent citations

Radio frequency breakdown between structured parallel plate electrodes with a millimetric gap in low pressure gases B. Legradic et al

-

Drift velocities and characteristic energies of electrons in deuterium at low and moderate E/N

W Roznerski et al -

Optical studies of pre-breakdown electron avalanches

Blevin, H. A. and Fletcher, J.

-

This content was downloaded from IP address 153.19.58.251 on 20/01/2018 at 19:30

(2)

J. Phys. D: Appl. Phys. 23 (1990) 1461-1463. Printed in the UK

RAPID COMMUNICATION

The characteristic energy and ratio of longitudinal diffusion coefficient to

mobility for electrons in hydrogen and

1 ^nitrogen

W Rotnerski, J Mechlinska-Drewko and K Leja

Department of Technical Physics and Applied Mathematics, Technical University of Gdansk, 80-952 Gdansk, Majakowskiego 11 11 2, Poland

Received 30 July 1990

Abstract. Using the Townsend-Huxley technique both the characteristic energy ( D / p ) and ratio of longitudinal diffusion coefficient to mobility DL/y for electrons in hydrogen and nitrogen have been determined, at ambient temperature over ranges of reduced electric field E / N : 70 S E / N S 1500 Td and 40 G E/N S 750 Td for hydrogen and nitrogen respectively. The results of the present work have been compared with some approachable experimental and theoretical data.

Since the Townsend-Huxley method (Huxley and Crompton 1974) yields results of high accuracy (Crompton et a1 1965), this experimental technique has been applied in this work to determine both the characteristic energy and ratio of longitudinal diffusion coefficient to mobility. In the Townsend-Huxley method, the thermal electrons emitted from a source of a small size diffuse through a gas in a homogeneous electric field and are collected by an anode. Actually, this technique depends on the measurement of the ratios of the currents arriving at the coaxial segments of a divided anode. In the present version of the exper- iment the following form of the expression for the fraction R of the total current falling onto the central part of an anode has been used (Huxley and Crompton

1974) :

where

A L = W / 2 D L

p

⁼AL(1 - 2CY/AL)"2

The quantities b. c , h , CY, W , D and DL are the radius of the central disc, the external radius of the anode.

the length of diffusion space, the drift velocity, the ionization coefficient and the transverse and longitudinal coefficients, respectively.

A suitable use of the expressions (1) allows us to take into account any other version of anode as well.

Measuring the current ratios at various pressures and geometrical variants of the anode. for each € I N reduced electric field value, we form the system of equations ( l ) , and subsequently a suitable numerical procedure gives both the characteristic energy D/,u and the ratio of longitudinal diffusion coefficient to mobility D L / p as the solution. Because the quantity R is a very slowly changing function of DL/,u, generally the use of a considerable number of the equations (1) is necess- ary.

The results of the present work are illustrated in three figures. Figure 1 shows the results of this work in hydrogen up to 1500Td. We noticed that our D L / p data agree fairly well with those of Blevin et a1 (1976) over the common E / N range. The present D L / p results also agree well up to 1OOOTd with those of Saelee and Lucas (1977). As to the characteristic energy for

hydrogen, our D / p results are in very good agreement with those of Crompton et a1 (1965). It is worth adding that the difference between the two sets of data

0022-3727:90;111461

+

^{03 $03.50}

⁰

1990 IOP Publishing Ltd 1461

(3)

Rapid communication

i

0 1

1

MO 1000

E / N ITd)

1500

Figure 1. Characteristic energy D / p and the DLlp

coefficient as a function of E / N in hydrogen up to 1500 Td.

D / p : 0 , present results; V, Saelee and Lucas (1977); m, present results.

between 70 and 200Td does not exceed 3.3%. In figures 2 and 3 the results of the present work for nitrogen are presented. Our DL/p results (figure 2) agree very well with those of Wedding et a1 (1985) between 200 and 300Td, and those of Fletcher and Reid (1980) for E / N between 400 and 500Td.

Although not presented in figure 2, the experimental data of Nakamura (1987) agree with ours within the combined errors of the two data sets.

We observed, however, some discrepancies between our DL/p results and those of Saelee et a1 (1977). The points of the latter work lie higher (except one point for 566 Td). and the largest difference between both sets of data reaches about 25% at 266 Td.

Figure 3 shows a good agreement of our results with the experimental data of Fletcher and Reid (1980) and

0

l

200 400 600

E/N l Td I

Figure 2. Ratio of longitudinal diffusion coefficient to mobility (DLip) as a function of E / N in nitrogen up to 750Td. 0, Saelee et a/ (1977); 0, Fletcher and Reid (1980); A , Wedding et a / (1985); N, present results.

l I

0 200 400 600 800

E/N (Td)

Figure 3. Ratio of transverse diffusion coefficient to mobility ( D l p ) as a function of E / N up to 750 Td in nitrogen. A , Kontoleon et a/ (1 973); 0, Fletcher and Reid (1980); 0, Wedding et a/ (1985); 0 , present results.

Kontoleon et a1 (1973), except for the point at 566 Td in the latter work. The difference between the results of the present work and those of Wedding et a1 (1985) increases up to about 10% for E / N > 350 Td.

The present D / p and D L / p data agree fairly well with the Boltzmann and Monte Carlo results of Pene- trante and Bardsley (1984) for E / N = 70 and 100 Td, and Braglia et a1 (1985) for 150 and 200 Td. For E / N < 50 Td our results disagree with the data of the theoretical work quoted above, and discrepancies are larger than the estimated error of the present work while the all-experimental results mentioned earlier agree with each other over the common E / N ranges, at least in the limit of combined errors of the experimental data sets. The fact that all experimental results have been obtained using various measurement tech- niques raises the degree of their reliability (as a common experimental data set). It seems that the reason for the discrepancies described above is probably the lack of a consistent set of cross sections for nitrogen.

The authors would like to thank Mr R Barczynski for his valuable and willing help in elaborating the numerical part of this work.

The present work was supported in part under pro- ject CPBP 01.06.

References

Blevin H A , Fletcher J and Hunter S R 1976 J. Phys. D:

A p p l . Phys. 9 1671

Braglia G L, Wilhelm J and Winkler R 1985 Lett. Nuooo Cimento 44 257

Crompton R W , Elford M T and Gascoigne J 1965 Aust. J . Phys. 18 409

Crompton R W , Liley B S, McIntosh A I and Hurst C A 1965 Proc. 7th ICPIG (Beograd) v01 1 (Beograd:

Gradevinsha Knjiga Publishing House) p 86

Fletcher J and Reid I D 1980 J . Phys. D: A p p l . Phys. 13 2275

Huxley L G H and Crompton R W 1974 The Diffusion and Drift of Electrons in Gases (New York: Wiley)

1462

(4)

Rapid communication

Kontoleon N , Lucas J and Virr L E 1973 J. _Phys.D: Appl. Saelee H T and Lucas J 1977 J. _Phys.D: Appl. Phys. 10 Nakamura Y 1987 J. Phys. D: Appi. Phys. 20 933 Saelee H T, Lucas J and Limbeek J W 1977 Solid State Penetrante B M and Bardsley J N 1984 J. _Phys.D: Appl. Electron. Deu. 1 111

Appl. Phys. 18 2361

Phys. 6 1237 343

Phys. 17 1971 Wedding A B, Blevin H A and Fletcher J 1985 J. Phys. D:

1463